question_answer

A fish, looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the surface of water, the radius of the circle in centimetre is:

A)  \[\frac{12\times 3}{\sqrt{5}}\]                 

B)  \[12\times 3\times \sqrt{5}\]

C)  \[\frac{12\times 3}{\sqrt{7}}\]                 

D)  \[12\times 3\times \sqrt{7}\]

Correct Answer: C

Solution :

From figure tan \[C=\frac{r}{12}\] or            \[r=12\] or            \[r=\frac{12\sin C}{\sqrt{1-{{\sin }^{2}}C}}\]                 \[r=\frac{12\times \frac{1}{\mu }}{\sqrt{1-\frac{1}{{{\mu }^{2}}}}}=\frac{12}{\sqrt{{{\mu }^{2}}-1}}=\frac{12}{\sqrt{{{\left( \frac{4}{3} \right)}^{2}}-1}}\]                 \[i.e.,\] \[r=\frac{12\times 3}{\sqrt{7}}\]